• question_answer The real values of $x$and$y$for which the equation is $(x+iy)$ $(2-3i)$= $4+i$ is satisfied, are [Roorkee 1978] A) $x=\frac{5}{13},y=\frac{8}{13}$ B) $x=\frac{8}{13},y=\frac{5}{13}$ C) $x=\frac{5}{13},y=\frac{14}{13}$ D) None of these

Equation $(x+iy)(2-3i)=4+i$ Þ  $(2x+3y)+i(-3x+2y)=4+i$ Equating real and imaginary parts, we get $2x+3y=4$    ......(i) $-3x+2y=1$ ......(ii) From (i) and (ii), we get $x=\frac{5}{13},y=\frac{14}{13}$ Aliter: $x+iy=\frac{4+i}{2-3i}=\frac{(4+i)(2+3i)}{13}=\frac{5}{13}+\frac{14}{13}i$ .